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A209697 Triangle of coefficients of polynomials u(n,x) jointly generated with A209698; see the Formula section. 3
1, 0, 2, 0, 2, 4, 0, 3, 6, 8, 0, 4, 10, 16, 16, 0, 5, 15, 30, 40, 32, 0, 6, 21, 50, 84, 96, 64, 0, 7, 28, 77, 154, 224, 224, 128, 0, 8, 36, 112, 258, 448, 576, 512, 256, 0, 9, 45, 156, 405, 810, 1248, 1440, 1152, 512, 0, 10, 55, 210, 605, 1362, 2420, 3360, 3520 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..64.

FORMULA

u(n,x)=x*u(n-1,x)+x*v(n-1,x),

v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

0...2

0...2....4

0...3....6...8

0...4...10...16...16

First three polynomials v(n,x): 1, 2x, 2x + 4x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];

v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]   (* A209697 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]   (* A209698 *)

CROSSREFS

Cf. A209698, A208510.

Sequence in context: A209699 A115273 A194759 * A126440 A131186 A137312

Adjacent sequences:  A209694 A209695 A209696 * A209698 A209699 A209700

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified October 22 18:17 EDT 2019. Contains 328319 sequences. (Running on oeis4.)